McCoy suffered a left hamstring injury in practice on Aug. 18. The source told Anderson that McCoy's MRI showed what was described internally as a "small tear," adding: "They say it tore in a spot where it couldn't have been any better for us. It tore in a spot that is kind of high up, surrounded by stronger muscles in the glutes and things like that."
Bills coach Rex Ryan had said on Aug. 21 that he was "cautiously optimistic" that McCoy would be ready for the opener. Ryan did not reveal the results of McCoy's MRI when he made his comments.
But earlier this week, Ryan cast some doubt on whether McCoy would be able to play, saying, "well, we certainly expect him to be ready to go, I hope," adding that the Bills would rely on the "next man" if he can't play.
According to the source, McCoy is not at full speed in practice but is doing rehab work, including light footwork, agility and cardio conditioning, but there is concern he won't be in great "football shape."
"It's way too early to say whether [McCoy] will play or not. He is doing a little bit more every day. But hell yes, I'm concerned about that," the source said. "I can't say for sure he's going to be with us Week 1. I can't say that at all. It will take everything we got just to get him ready for game day, and then [when] we get to game day, [there's] no way he can be in great football shape. So I think he will be on a pitch count, I think at the very best.
"I mean, if he came around and just started feeling really, really good, heaven knows. But [we] have to look at all the contingency plans: putting him on a pitch count possibly, or, he's not out there at all and we got to go without him and get the other guys ready. You just don't know."
The source emphasized that the team is "still game planning for him to be ready. We're hoping he will be ready, but I can't sit here and tell you that he will be ready."
If McCoy is not 100 percent, "I would recommend that he doesn't play because [we] need him for the rest of the year," the source said. "[We] don't need him at 75 percent and risk losing him down the line."
"You know he is a Ferrari and for him to be hitting on all cylinders, that thing has got to be right," the source told Anderson.
The Bills released Fred Jackson this week, leaving the team with an unsettled backfield as it prepares for its regular-season opener Sept. 13 against the Indianapolis Colts.
McCoy has remained out of practice with his injury. Bryce Brown (hamstring) and Boobie Dixon (calf) returned to practice last week but did not play in Saturday's preseason game. Rookie running back Karlos Williams also remained out of practice last week after an undisclosed medical procedure.
ESPN.com's Mike Rodak contributed to this report.